Abstract
In this paper, a new categorical crystal structure for the quantum affine algebras is presented. We introduce the notion of extended crystals Bg(∞) for an arbitrary quantum group Uq(g), which is the product of infinite copies of the crystal B(∞). For a complete duality datum D in the Hernandez–Leclerc category Cg0 of a quantum affine algebra Uq′ (g), we prove that the set BD(g) of the isomorphism classes of simple modules in Cg0 has an extended crystal structure isomorphic to Bbgfin(∞). An explicit combinatorial description of the extended crystal BD(g) for affine type A(1)n is given in terms of affine highest weights.
Original language | English |
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Pages (from-to) | 223-267 |
Number of pages | 45 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 2022 |
Issue number | 792 |
DOIs | |
State | Published - 1 Nov 2022 |